Q18.10P - Chemistry: Molecular Nature Of Matter And Change

Question

Write the  expression for each of the following in water: 

(a) ${\mathbf{\text{CH}}}_{\mathbf{\text{3}}}{\mathbf{\text{NH}}}_{\mathbf{\text{3}}}^{\mathbf{\text{+}}}$

(b)  $\mathbf{\text{HClO}}$

(c)  ${\text{H}}_{\text{2}}\text{S}$

Step-by-Step Solution

Answer

(a) The $K_a$expression for ${\text{CH}}_{\text{3}}{\text{NH}}_{\text{3}}^{\text{+}}$is ${\text{K}}_{\text{a}}\text{ = }\frac{{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][CH}}_{\text{3}}{\text{NH}}_{\text{2}}\text{]}}{{\text{[CH}}_{\text{3}}{\text{NH}}_{\text{3}}^{\text{+}}\text{]}}$.

(b) The$K_a$ expression for$HClO$ is${\text{K}}_{\text{a}}\text{ = }\frac{{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][ClO}}^{\text{-}}\text{]}}{\text{[HClO]}}$ .

(c) The $K_a$expression for ${\text{H}}_{\text{2}}\text{S}$is${\text{K}}_{\text{a}}\text{ = }\frac{{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][HS}}^{\text{-}}\text{]}}{{\text{[H}}_{\text{2}}\text{S]}}$ .

Step 1: Concept Introduction

The acid dissociation constant  $\mathbf{\left(}{\mathit{K}}_{\mathbf{a}}\mathbf{\right)}$is a numerical representation of an acid's strength in solution. The dissociation constant ${\text{K}}_{\text{a}}\text{ = }\frac{{\text{[A}}^{\text{-}}{\text{][H}}^{\text{+}}\text{]}}{\text{[HA]}}$  is commonly stated as a quotient of the equilibrium concentrations (in$\mathit{m}\mathit{o}\mathit{l}\mathbf{/}\mathit{L}$ ). 

Step 2: K a expression for CH 3 NH 3 +

(a)

To write the $K_a$expression of ${\text{CH}}_{\text{3}}{\text{NH}}_{\text{3}}^{\text{+}}$in water, we should write the balanced reaction first –

${\text{CH}}_{\text{3}}{\text{NH}}_{\text{3}}^{\text{+}}{\text{(aq) + H}}_{\text{2}}\text{O(l) }\rightleftharpoons {\text{ H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{(aq) + CH}}_{\text{3}}{\text{NH}}_{\text{2}}\text{(aq)}$

Then write the $K_a$expression using the formula below. Note that it only includes aqueous species.

$\begin{array}{c}{\text{K}}_{\text{a}}\text{ = }\frac{\text{[product]}}{\text{[reactant]}}\\ {\text{K}}_{\text{a}}\text{ = }\frac{{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][CH}}_{\text{3}}{\text{NH}}_{\text{2}}\text{]}}{{\text{[CH}}_{\text{3}}{\text{NH}}_{\text{3}}^{\text{+}}\text{]}}\end{array}$

 

Therefore, the expression is obtained as .${\text{K}}_{\text{a}}\text{ = }\frac{{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][CH}}_{\text{3}}{\text{NH}}_{\text{2}}\text{]}}{{\text{[CH}}_{\text{3}}{\text{NH}}_{\text{3}}^{\text{+}}\text{]}}$

Step 3: K a expression for H C l O

(b)

To write the$K_a$ expression of $HClO$in water, we should write the balanced reaction first –

${\text{HClO(aq) + H}}_{\text{2}}\text{O(l) }\rightleftharpoons {\text{ H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{(aq) + ClO}}^{\text{-}}\text{(aq)}$

Then write the $K_a$expression using the formula below. Note that it only includes aqueous species.

$\begin{array}{c}{\text{K}}_{\text{a}}\text{ = }\frac{\text{[product]}}{\text{[reactant]}}\\ {\text{K}}_{\text{a}}\text{ = }\frac{{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][ClO}}^{\text{-}}\text{]}}{\text{[HClO]}}\end{array}$

 

Therefore, the expression is obtained as .${\text{K}}_{\text{a}}\text{ = }\frac{{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][ClO}}^{\text{-}}\text{]}}{\text{[HClO]}}$

Step 4: K a expression for H 2 S

(c)

To write the$K_a$ expression of in water, we should write the balanced reaction first –

${\text{H}}_{\text{2}}{\text{S(aq) + H}}_{\text{2}}\text{O(l) }\rightleftharpoons {\text{ H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{(aq) + HS}}^{\text{-}}\text{(aq)}$

Then write the$K_a$ expression using the formula below. Note that it only includes aqueous species.

$\begin{array}{c}{\text{K}}_{\text{a}}\text{ = }\frac{\text{[product]}}{\text{[reactant]}}\\ {\text{K}}_{\text{a}}\text{ = }\frac{{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][HS}}^{\text{-}}\text{]}}{{\text{[H}}_{\text{2}}\text{S]}}\end{array}$

 

Therefore, the expression is obtained as .${\text{K}}_{\text{a}}\text{ = }\frac{{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][HS}}^{\text{-}}\text{]}}{{\text{[H}}_{\text{2}}\text{S]}}$